How do you simplify 3sqrt( (27 + 1 ))?

1 Answer
Mar 11, 2018

See a solution process below:

Explanation:

First, rewrite the expression within the radical as:

3sqrt(27 + 1) => 3sqrt(28) => 3sqrt(4 * 7)

Now, use this rule for radicals to simplify the radical:

sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))

3sqrt(color(red)(4) * color(blue)(7)) =>

3sqrt(color(red)(4)) * sqrt(color(blue)(7)) =>

3 * 2 * sqrt(color(blue)(7)) =>

6sqrt(color(blue)(7))